Question

a class of 30 students took midterm science exams. 20 students passed the chemistry exam, 14 students passed physics, and 6 students passed both chemistry and physics. which venn diagram correctly represents this information? select the correct answer.

Explanation:

Step1: Recall Venn - diagram concept

In a Venn - diagram for two sets (Chemistry and Physics), the number of students who passed Chemistry is the sum of those who passed only Chemistry and those who passed both. The number of students who passed Physics is the sum of those who passed only Physics and those who passed both.

Step2: Analyze the given data

We know that the number of students who passed Chemistry ($n(C)$) = 20, the number of students who passed Physics ($n(P)$) = 14, and the number of students who passed both ($n(C\cap P)$) = 6. The number of students who passed only Chemistry is $n(C)-n(C\cap P)=20 - 6=14$, and the number of students who passed only Physics is $n(P)-n(C\cap P)=14 - 6 = 8$.

Step3: Match with Venn - diagrams

In Venn - diagram 3, the number in the Chemistry - only part is 14, the number in the Physics - only part is 8, and the number in the intersection is 6.

Answer:

Venn diagram 3